{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# p10: Polynomials and corresponding equipotential curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='svg'\n",
    "from numpy import pi,linspace,arange,abs,cos,poly,polyval,meshgrid,real,imag\n",
    "from matplotlib.pyplot import figure,subplot,plot,title,axis,contour"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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   ],
   "source": [
    "N = 16\n",
    "figure(figsize=(9,8))\n",
    "for i in range(2):\n",
    "    if i==0:\n",
    "        s = 'equispaced points'; x = -1.0 + 2.0*arange(0,N+1)/N\n",
    "    if i==1:\n",
    "        s = 'Chebyshev points'; x = cos(pi*arange(0,N+1)/N)\n",
    "    p = poly(x)\n",
    "    # Plot p(x)\n",
    "    xx = linspace(-1.01,1.01,400,True)\n",
    "    pp = polyval(p,xx)\n",
    "    fig = subplot(2,2,2*i+1)\n",
    "    plot(x,0*x,'o',xx,pp)\n",
    "    fig.set_xlim(-1,1)\n",
    "    title(s)\n",
    "    \n",
    "    # Plot equipotential curves\n",
    "    subplot(2,2,2*i+2)\n",
    "    plot(real(x),imag(x),'o')\n",
    "    axis([-1.4,1.4,-1.12,1.12])\n",
    "    xgrid = linspace(-1.4,1.4,250,True)\n",
    "    ygrid = linspace(-1.12,1.12,250,True)\n",
    "    xx,yy = meshgrid(xgrid,ygrid)\n",
    "    zz = xx + 1j*yy\n",
    "    pp = polyval(p,zz)\n",
    "    levels = 10.0**arange(-4,1)\n",
    "    contour(xx,yy,abs(pp),levels)\n",
    "    title(s)"
   ]
  }
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